Key Point Extraction the best method?
The 2nd method would make sense only if your object is at the same position in all test images. You would have such situation if you operated on crops located by a separate object detection algorithm. This happens to be the case in facial key-point detection. 

The 1st method would be much more robust to various object poses since it is translation covariant by design. If a keypoint is detected at location A, it will be equally well detected at any other position with the same set of parameters.